A number of filamentous biopolymers including actin filaments (F-actin
), microtubules (MT), tobacco mosaic virus (TMV), and the filamentous
bacteriophage fd form bundles under vc ell-defined conditions. All of
these macromolecules are negatively charged rodlike assemblies, and la
teral association is induced by a number of cations such as divalent a
nd trivalent metal ions and homopolymers of basic peptides. The genera
l features of bundle formation are largely independent of the specific
structure of the biopolymers and the bundling agent used. They are al
so approximately independent of the concentration of macromolecules. H
owever, a threshold concentration of bundling agent is required in ord
er to form large lateral aggregates, detected by a sharp increase in l
ight scattering and by electron microscopy. The threshold concentratio
n varies strongly with the valence of the cations and increases with t
he ionic strength of the solution. The formation of bundles is reversi
ble by polyanions such as nucleoside phosphates. This overall behavior
is similar to the phenomenon of DNA condensation and can be explained
by applying polyelectrolyte theories, including the concept of counte
rion condensation. Our results provide quantitative comparisons with a
number of predictions of polyelectrolyte theories, including the calc
ulation of apparent binding affinity and its dependence on ionic stren
gth. They also support the prediction of an attractive interaction bet
ween the neighboring Filaments due to sharing of counterion clouds. In
addition, the simply detectable, reversible assembly of macromolecule
s in solution serves as a sensitive indicator of the active associatio
n of small ions and the formation of ion clusters. Association constan
ts of Co(NH3)(6)(3+)-ATP and Lys(18)-ATP were determined by applicatio
n of this model.